Many digital modulation schemes in current use are memoryless, meaning that the modulated signal within a particular time interval (called the symbol duration), corresponding to a particular data bit or group of data bits, is independent of the modulated signal for all other symbol durations. Some well-known examples of memoryless modulation schemes include binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), and quadrature amplitude modulation (QAM). In this context a modulation scheme refers to the modulation and corresponding demodulation protocols or methods which are implemented in modulators and demodulators.
In contrast, a modulation scheme with memory produces a modulated signal that depends not only on the current bit (or group of bits), but also on previous bits or groups of bits. In this case the modulators and demodulators include a memory or register for storing previously transmitted or received bits or symbols. One particular class of modulation schemes with memory (ie non-memoryless) are recursive modulation schemes. These are modulation schemes with memory, defined recursively. Recursive modulators are characterised by their use of feedback within the modulator structure, in which the modulator output depends not only on current and previous data bits, but also on previous modulator outputs (or more generally on previous values of internal state variables). Notable examples of recursive modulation schemes are differential modulation in which the data is modulated onto differences between successive symbols, and continuous phase modulation where a recursive modulator is used to ensure constant amplitude and continuous phase properties. For example in differential modulation a transmitted bit is obtained by binary (ie mod 2) addition of the previously transmitted bit and the bit to be transmitted (ie yi=yi−1⊕xi). Similarly on the receive (or decoding) side, the bit to be decoded is the binary addition of the received bit and the previously received bit (ie xi=yi⊕yi−1).
Differential modulation schemes, such as differential phase shift keying (DPSK), are an attractive choice for situations where the absolute phase of the received signal is unknown, or is difficult to recover. The data is modulated onto the phase difference between successive symbols, rather than an absolute phase. Note that all differential modulation schemes are recursive (that is their modulator includes a feedback loop).
Advantages of differential modulation schemes include that it is possible to implement a non-coherent demodulator that does not need to perform computationally expensive carrier phase recovery. This can greatly decrease the implementation complexity of the receiver. Another advantage is that only a modest change is required at the transmitter to achieve the differential modulation. Disadvantages of differential modulation include that a single symbol erasure can affect the subsequent symbol(s), since the demodulator needs to know the phase difference between adjacent symbols. A further disadvantage is a 3 dB loss in performance when non-coherent demodulation is used.
Many variations of differential modulation schemes are possible, by varying the set of possible phase changes, and by varying the mapping between bits and phase changes. Differential modulation schemes are used in a wide variety of wired, radio frequency wireless and optical wireless communication systems. Common examples include differential binary phase shift keying (DBPSK), differential quaternary phase shift keying (DQPSK), or other variants such as π/4 offset differential quaternary phase shift keying (π/4-DQPSK).
In many circumstances it may be desirable to use a continuous phase modulation scheme (CPM). CPM provides higher spectral efficiency compared to other modulation schemes such as Phase Shift Keying (PSK) and a constant modulus allows the use of lower cost amplifiers since less headroom needs to be supplied. However there are also disadvantages associated with CPM. These include a higher complexity demodulator and the potential for catastrophic error propagation. For example if one symbol is “erased” all subsequent symbols are also erased. CPM is used in a wide range of systems including cellular communications systems such as GSM, automatic identification system (AIS), satellite communications, and various others. One widely used version of CPM is Gaussian minimum shift keying (GMSK).
It is desirable to increase the reliability of digital communication systems by using forward error control coding. The general advantages include increased spectral efficiency, increased power efficiency, and greatly decreased bit error rate (BER) or word error rate of the decoded signal. Modern error control codes such as turbo codes or low density parity check codes can offer performance that approach fundamental limits set by information theory.
One modern code which offers very good performance and has several implementation advantages is the irregular repeat accumulate (IRA) code. These codes have a low-complexity encoder implementation and a low complexity iterative decoding algorithm. These codes can approach the Shannon capacity of many channels.
FIG. 1 is a functional block diagram for implementing an Irregular Repeat Accumulate (IRA) code 10 by an encoder module in a transmitter. As shown in FIG. 1, an IRA code consists of the serial concatenation of an irregular repeat code encoder module 1, an interleaver module 2, a parity check module 3 and an accumulator module 5. As shown in FIG. 1, the IRA encoder receives a plurality of source bits u=(u1 . . . , uk) 6 and generates a plurality of encoded bits x=(x1, . . . , xn) 9. The combination of the irregular repeat code, interleaver and irregular parity checks can be viewed without loss of generality as a low density generator matrix (LDGM) code 4. By itself however, an LDGM code offers poor performance due to the existence of very low weight code-words. Concatenation of the outer LDGM encoder with a non-recursive inner code replacing the accumulator would also give very poor performance.
The key to the high performance of the IRA code 10 is the recursive nature of the accumulator 5 which combines 7 adjacent coded symbols (or encoded bits) d 8 to generate encoded bits x 9 for transmission. This ensures convergence of an iterative decoder which passes soft information between two component decoders (a) the LDGM decoder and (b) the accumulator decoder. The output of an irregular repeat accumulate code could be used to modulate the baseband channel input, using any suitable modulation scheme such as PSK, PAM, QAM, DPSK, DQPSK or CPM. However, if recursive (ie non-memoryless) modulation schemes are used (eg DPSK, DQPSK or CPM), it is standard practice to insert an additional interleaver 11 at the output of the accumulator 5 and prior to the modulator 12. This is shown in FIG. 2.
The additional interleaver 11 is required to ensure convergence of a decoder 20 that now iterates, passing soft information between three component decoders: (a) the variable node decoder 18; (b) the check node/accumulator decoder 16; and (c) a soft demodulator 14. This decoder structure is shown in FIG. 2 which is a functional block diagram of a transmitter and receiver for encoding and decoding an IRA code with recursive modulation. The addition of the interleaver 11 adds to the complexity and cost of the transmitter and receiver (which is required to include a corresponding de-interleaver, marked as blocks 15 and 17 in FIG. 2) in such systems. An additional consideration with this decoder structure is the order of activation of the three different component decoders. This adds to the complexity of the decoder, and may require additional control logic in order to optimise the order of activation. Alternatively, a fixed activation schedule could be used at the expense of decreased performance.
These requirements add additional cost and complexity and thus there is a need to develop coding methods and apparatus for systems using LDGM codes with recursive modulation schemes that are simpler and cheaper to implement, or to at least provide a useful alternative to existing methods and apparatus.